Journal of Approximation Theory最新文献

英文中文

Best constants in a class of Landau type inequalities 一类朗道型不等式的最佳常数

IF 0.6 3区数学 Q2 MATHEMATICS

Journal of Approximation Theory

Pub Date : 2026-01-22 DOI: 10.1016/j.jat.2026.106285

JinYan Miao, Silvestru Sever Dragomir

<div><div>We first prove the best constant <math><mi>C</mi></math> in a Landau type inequality <math><mrow><msubsup><mrow><mo>‖</mo><msup><mrow><mi>f</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>‖</mo></mrow><mrow><mi>∞</mi></mrow><mrow><mn>5</mn></mrow></msubsup><mo>≤</mo><mi>C</mi><msubsup><mrow><mo>‖</mo><mi>f</mi><mo>‖</mo></mrow><mrow><mi>∞</mi></mrow><mrow><mn>3</mn></mrow></msubsup><msub><mrow><mo>‖</mo><msup><mrow><mi>f</mi></mrow><mrow><mo>′</mo><mo>′</mo></mrow></msup><mo>‖</mo></mrow><mrow><mi>∞</mi></mrow></msub><msub><mrow><mo>‖</mo><msup><mrow><mi>f</mi></mrow><mrow><mo>′</mo><mo>′</mo><mo>′</mo></mrow></msup><mo>‖</mo></mrow><mrow><mi>∞</mi></mrow></msub><mo>,</mo></mrow></math>and with similar approach, we prove the best constants in a more general form <math><mrow><msubsup><mrow><mo>‖</mo><msup><mrow><mi>f</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>‖</mo></mrow><mrow><mi>∞</mi></mrow><mrow><mn>2</mn><mo>+</mo><mi>η</mi></mrow></msubsup><mo>≤</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>η</mi></mrow></msub><msubsup><mrow><mo>‖</mo><mi>f</mi><mo>‖</mo></mrow><mrow><mi>∞</mi></mrow><mrow><mn>1</mn><mo>+</mo><mi>η</mi></mrow></msubsup><msubsup><mrow><mo>‖</mo><msup><mrow><mi>f</mi></mrow><mrow><mo>′</mo><mo>′</mo></mrow></msup><mo>‖</mo></mrow><mrow><mi>∞</mi></mrow><mrow><mn>1</mn><mo>−</mo><mi>η</mi></mrow></msubsup><msubsup><mrow><mo>‖</mo><msup><mrow><mi>f</mi></mrow><mrow><mo>′</mo><mo>′</mo><mo>′</mo></mrow></msup><mo>‖</mo></mrow><mrow><mi>∞</mi></mrow><mrow><mi>η</mi></mrow></msubsup></mrow></math>for all <math><mrow><mn>0</mn><mo>≤</mo><mi>η</mi><mo>≤</mo><mn>1</mn></mrow></math>. Here we have the direct expression for each of the best constants <math><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi>η</mi></mrow></msub><mo>=</mo><mfrac><mrow><msubsup><mrow><mi>θ</mi></mrow><mrow><mi>η</mi></mrow><mrow><mi>η</mi></mrow></msubsup><msup><mrow><mrow><mo>(</mo><mn>1</mn><mo>−</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>η</mi></mrow></msub><mo>)</mo></mrow></mrow><mrow><mn>2</mn><mo>+</mo><mi>η</mi></mrow></msup></mrow><mrow><mn>2</mn><msup><mrow><mrow><mo>(</mo><mn>1</mn><mo>/</mo><mn>4</mn><mo>−</mo><msubsup><mrow><mi>θ</mi></mrow><mrow><mi>η</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>/</mo><mn>3</mn><mo>)</mo></mrow></mrow><mrow><mn>1</mn><mo>+</mo><mi>η</mi></mrow></msup></mrow></mfrac><mo>,</mo></mrow></math>where <math><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi>η</mi></mrow></msub><mo>=</mo><mfrac><mrow><mn>3</mn><mo>+</mo><mn>3</mn><mi>η</mi><mo>−</mo><msqrt><mrow><mo>−</mo><mn>3</mn><msup><mrow><mi>η</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mn>6</mn><mi>η</mi><mo>+</mo><mn>9</mn></mrow></msqrt></mrow><mrow><mn>8</mn><mo>+</mo><mn>4</mn><mi>η</mi></mrow></mfrac><mo>.</mo></mrow></math>A Landau type inequality and another special cas

我们首先证明了朗道型不等式‖f′‖∞5≤C‖f′∞3‖f′′∞‖f′′′∞‖∞的最佳常数C，并用类似的方法证明了对于所有0≤η≤1‖f′′∞‖∞2+η≤Cη‖f′∞1+η‖f′′‖∞η的更一般形式的最佳常数C。这里我们得到了各最佳常数Cη=θηη(1−θη)2+η2(1/4−θη2/3)1+η的直接表达式，其中θη=3+3η−−3η2−6η+98+4η。也可以从这种一般形式推导出朗道不等式和朗道-柯尔莫哥洛夫不等式的另一种特殊情况（希洛夫结果），并具有最佳常数。

引用次数: 0

Lower bounds on the Haraux function 哈罗函数的下界

IF 0.6 3区数学 Q2 MATHEMATICS

Journal of Approximation Theory

Pub Date : 2026-01-22 DOI: 10.1016/j.jat.2026.106284

Patrick L. Combettes, Julien N. Mayrand

The Haraux function is an important tool in monotone operator theory and its applications. One of its salient properties for a maximally monotone operator is to be valued in

[0, + \infty]

and to vanish only on the graph of the operator. Sharper lower bounds for this function have been proposed in specific cases. We derive lower bounds in the general context of set-valued operators in reflexive real Banach spaces. These bounds are new, even for maximally monotone operators acting on Euclidean spaces, a scenario in which we show that they can be better than existing ones. As a by-product, we obtain lower bounds on the Fenchel–Young function in variational analysis. Several examples are given and applications to composite monotone inclusions are discussed.

Haraux函数是单调算子理论及其应用中的一个重要工具。极大单调算子的一个显著性质是值在[0，+∞]范围内，并且只在算子的图上消失。在特定情况下，已经提出了这个函数的更清晰的下界。在自反实数Banach空间中，导出集值算子的下界。这些边界是新的，即使对于作用于欧几里得空间的极大单调算子，我们证明它们可以比现有的更好。作为一个副产品，我们得到了变分分析中fenchell - young函数的下界。给出了几个例子，并讨论了其在复合单调夹杂物中的应用。

引用次数: 0

Anisotropic approximation on space–time domains 时空域的各向异性近似

IF 0.6 3区数学 Q2 MATHEMATICS

Journal of Approximation Theory

Pub Date : 2026-01-08 DOI: 10.1016/j.jat.2025.106282

Pedro Morin , Cornelia Schneider , Nick Schneider

We investigate anisotropic (piecewise) polynomial approximation of functions in Lebesgue spaces as well as anisotropic Besov spaces. For this purpose we study temporal and spatial moduli of smoothness and their properties. In particular, we prove Jackson- and Whitney-type inequalities on Lipschitz cylinders, i.e., space–time domains

I \times D

with a finite interval

I

and a bounded Lipschitz domain

D \subset R^{d}

d \in N

. As an application, we prove a direct estimate result for adaptive space–time finite element approximation in the discontinuous setting.

研究了Lebesgue空间和Besov空间中函数的各向异性（分段）多项式逼近。为此，我们研究了平滑度的时间模量和空间模量及其性质。特别地，我们证明了Lipschitz柱面上的Jackson-型不等式和whitney -型不等式，即具有有限区间I和有界Lipschitz域D∧Rd， D∈N的时空域I×D。作为应用，证明了不连续环境下自适应时空有限元逼近的一个直接估计结果。

引用次数: 0

Strictly positive definite functions of finite orders and multivariate polynomial interpolation 有限阶严格正定函数与多元多项式插值

IF 0.6 3区数学 Q2 MATHEMATICS

Journal of Approximation Theory

Pub Date : 2026-01-03 DOI: 10.1016/j.jat.2025.106283

Shelby Kilmer, Xingping Sun, Matthew Wright

We study strictly positive definite functions of finite orders on real inner product spaces. Via exploring new connections to theories of Chebyshev ranks and Schur polynomials, we obtain quantifiable conditions for such functions. To assist field scientists in selecting an ideal multivariate polynomial interpolant, we propose and study the notions of “interpolating rank” and “minimal seminorm interpolation.” We quantify both Chebyshev ranks and interpolating ranks in terms of the number of common zeros of a certain finite collection of Schur polynomials. As a byproduct, we develop a mechanism to construct positive-rank Chebyshev systems of which examples are scarce in the literature.

研究了实内积空间上有限阶严格正定函数。通过探索与切比雪夫秩和舒尔多项式理论的新联系，我们得到了这些函数的可量化条件。为了帮助野外科学家选择理想的多元多项式插值，我们提出并研究了“插值秩”和“最小半精插值”的概念。我们将切比雪夫秩和内插秩用一定有限的舒尔多项式集合的公零数来量化。作为一个副产品，我们开发了一种机制来构建正秩切比雪夫系统，这种系统的例子在文献中很少。

引用次数: 0

Edge detection with polynomial frames on the sphere 球面上多项式帧的边缘检测

IF 0.6 3区数学 Q2 MATHEMATICS

Journal of Approximation Theory

Pub Date : 2025-12-26 DOI: 10.1016/j.jat.2025.106279

Frederic Schoppert

In a recent article, we have shown that a variety of localized polynomial frames, including isotropic as well as directional spherical systems, are suitable for detecting jump discontinuities that lie along circles on the sphere. More precisely, such edges can be identified in terms of their position and orientation by the asymptotic decay of the frame coefficients in an arbitrary small neighborhood. In this paper, we will extend these results to discontinuities which lie along general smooth curves. In particular, we prove upper and lower estimates for the frame coefficients when the analysis function is concentrated in the vicinity of such a singularity. The estimates are given in an asymptotic sense, with respect to some dilation parameter, and they hold uniformly in a neighborhood of the smooth curve segment under consideration.

在最近的一篇文章中，我们已经证明了各种局部多项式框架，包括各向同性和定向球系统，适合于检测沿球体上的圆的跳跃不连续。更准确地说，这样的边缘可以通过任意小邻域内框架系数的渐近衰减来识别它们的位置和方向。在本文中，我们将这些结果推广到沿一般光滑曲线的不连续点。特别地，我们证明了当分析函数集中在奇异点附近时框架系数的上估计和下估计。给出了关于膨胀参数的渐近估计，它们在所考虑的光滑曲线段的邻域内一致成立。

引用次数: 0

On the image of the limit q-Durrmeyer operator 关于极限q-Durrmeyer算子的像

IF 0.6 3区数学 Q2 MATHEMATICS

Journal of Approximation Theory

Pub Date : 2025-12-26 DOI: 10.1016/j.jat.2025.106280

Sofiya Ostrovska, Mehmet Turan

The focus of this work is on the properties of the

q

-Durrmeyer operators

M_{n, q},

n \in N,

and

M_{\infty, q}

introduced, for

q \in (0, 1),

by V. Gupta and H. Wang. First, it is shown that, for each

f \in C [0, 1],

the sequence

{M_{n, q} f}_{n \in N}

converges to

M_{\infty, q} f

uniformly on

[0, 1]

with a rate not slower than

C_{q, f} q^{n}

, which refines the previously available result by V. Gupta and H. Wang, and implies the possibility of an analytic continuation for

M_{\infty, q} f

into a neighbourhood of

[0, 1] .

Further investigation shows that

M_{\infty, q} f

admits an analytic continuation as an entire function regardless of

f \in C [0, 1]

. Finally, the growth estimates for these functions are received and applied to describe the point spectrum of

M_{\infty, q} .

The paper also addresses the significant differences between the properties of

M_{\infty, q}

and the previously well-known limit

q

-Bernstein operator

B_{\infty, q} .

本文重点研究了V. Gupta和H. Wang对q∈(0,1)引入的q- durrmeyer算子Mn，q， n∈n和M∞，q的性质。首先，证明了对于每一个f∈C[0,1]，序列{Mn，qf}n∈n在[0,1]上一致收敛到M∞，qf，且收敛速度不慢于Cq，fqn，从而改进了V. Gupta和H. Wang先前的结果，并暗示了M∞，qf解析延拓到[0,1]邻域的可能性。进一步研究表明，无论f∈C[0,1]如何，M∞，qf都允许作为整个函数的解析延拓。最后，接收了这些函数的增长估计，并将其应用于描述M∞，q的点谱。本文还讨论了M∞，q与之前众所周知的极限q- bernstein算子B∞，q的性质之间的显著区别。

引用次数: 0

Weighted estimates for dyadic maximal operators 二进极大算子的加权估计

IF 0.6 3区数学 Q2 MATHEMATICS

Journal of Approximation Theory

Pub Date : 2025-12-23 DOI: 10.1016/j.jat.2025.106278

Ferenc Weisz , Guangheng Xie , Dachun Yang

Let

α, β \in (0, \infty)

and

U_{α, β}

be the dyadic maximal operator. In this article, the authors find some sufficient conditions on the indices

α, β

to guarantee the boundedness of the operators

U_{α, β}

on weighted Lebesgue spaces. These conditions in special weight case turn out to be necessary and hence are sharp in some sense. Moreover, the authors show that a weight

w

belongs to the Muckenhoupt weight class

A_{p}

p \in (1, \infty)

, if and only if the operator

U_{α, β}

is bounded on weighted

L^{p}

spaces. Furthermore, the authors establish the weighted vector-valued dyadic maximal inequality and the weighted weak-type

(1, 1)

estimate for the operators

U_{α, β}

. As applications, the authors obtain the convergence of Fejér means of Walsh–Fourier series of martingales in both pointwise and Musielak–Orlicz spaces. These main results in Musielak–Orlicz space case remedy a missing necessary assumption of Theorems 3.2 and 3.4 in Weisz et al. (2023).

设α，β∈(0,∞)，且Uα，β为二进极大算子。给出了在加权Lebesgue空间上，算子Uα，β在指标α，β上的有界性的充分条件。这些条件在特殊权重情况下是必要的，因此在某种意义上是尖锐的。进一步证明了权w属于Muckenhoupt权类Ap， p∈(1,∞)，当且仅当算子Uα，β在加权Lp空间上有界。进一步建立了算子Uα，β的加权向量值并矢极大不等式和加权弱型（1,1）估计。作为应用，作者得到了鞅的Walsh-Fourier级数在点向空间和Musielak-Orlicz空间中的fej均值的收敛性。Musielak-Orlicz空间情况下的这些主要结果弥补了Weisz et al.（2023）中定理3.2和3.4中缺失的必要假设。

{"title":"Weighted estimates for dyadic maximal operators","authors":"Ferenc Weisz , Guangheng Xie , Dachun Yang","doi":"10.1016/j.jat.2025.106278","DOIUrl":"10.1016/j.jat.2025.106278","url":null,"abstract":"<div><div>Let <math><mrow><mi>α</mi><mo>,</mo><mi>β</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></mrow></math> and <math><msub><mrow><mi>U</mi></mrow><mrow><mi>α</mi><mo>,</mo><mi>β</mi></mrow></msub></math> be the dyadic maximal operator. In this article, the authors find some sufficient conditions on the indices <math><mrow><mi>α</mi><mo>,</mo><mi>β</mi></mrow></math> to guarantee the boundedness of the operators <math><msub><mrow><mi>U</mi></mrow><mrow><mi>α</mi><mo>,</mo><mi>β</mi></mrow></msub></math> on weighted Lebesgue spaces. These conditions in special weight case turn out to be necessary and hence are sharp in some sense. Moreover, the authors show that a weight <math><mi>w</mi></math> belongs to the Muckenhoupt weight class <math><msub><mrow><mi>A</mi></mrow><mrow><mi>p</mi></mrow></msub></math>, <math><mrow><mi>p</mi><mo>∈</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></mrow></math>, if and only if the operator <math><msub><mrow><mi>U</mi></mrow><mrow><mi>α</mi><mo>,</mo><mi>β</mi></mrow></msub></math> is bounded on weighted <math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math> spaces. Furthermore, the authors establish the weighted vector-valued dyadic maximal inequality and the weighted weak-type <math><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></math> estimate for the operators <math><msub><mrow><mi>U</mi></mrow><mrow><mi>α</mi><mo>,</mo><mi>β</mi></mrow></msub></math>. As applications, the authors obtain the convergence of Fejér means of Walsh–Fourier series of martingales in both pointwise and Musielak–Orlicz spaces. These main results in Musielak–Orlicz space case remedy a missing necessary assumption of Theorems 3.2 and 3.4 in Weisz et al. (2023).</div></div>","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"315 ","pages":"Article 106278"},"PeriodicalIF":0.6,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145839928","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An electrostatic model for the roots of discrete classical orthogonal polynomials 离散经典正交多项式根的静电模型

IF 0.6 3区数学 Q2 MATHEMATICS

Journal of Approximation Theory

Pub Date : 2025-11-29 DOI: 10.1016/j.jat.2025.106256

Joaquín Sánchez-Lara

An electrostatic model is presented to describe the behaviour of the roots of classical discrete orthogonal polynomials. Indeed, this model applies more generally to the roots of polynomial solutions of second-order linear difference equations

A Δ_{h} \nabla_{h} y + B Δ_{h} y + C y = 0

where

A

B

and

C

are polynomials and

Δ_{h} f (x) = f (x + h) - f (x) and \nabla_{h} f (x) = f (x) - f (x - h)

with

h > 0

. The existence of a unique distribution of points which minimizes the energy of the system is guaranteed under some assumptions on

A

and

B

. Furthermore, interlacing properties and the monotonicity of the roots depending on the parameters which appear in the difference equation are obtained from this electrostatic model.

提出了一个静电模型来描述经典离散正交多项式根的行为。事实上，该模型更普遍地适用于二阶线性差分方程AΔh∇hy+BΔhy+Cy=0的多项式解的根，其中A， B和C是多项式，Δhf(x)=f(x+h) - f(x)和∇hf(x)=f(x) - f(x - h), h>0。在a和b上的一些假设条件下，保证了系统能量最小的点的唯一分布的存在性，并由此得到了差分方程中出现的参数的交错性和根的单调性。

引用次数: 0

Smoothness and time–frequency analysis in Sobolev–Besicovitch spaces of almost periodic functions 概周期函数Sobolev-Besicovitch空间的平滑性和时频分析

IF 0.6 3区数学 Q2 MATHEMATICS

Journal of Approximation Theory

Pub Date : 2025-11-25 DOI: 10.1016/j.jat.2025.106255

Juan Miguel Medina , Hernán D. Centeno , Raúl F. Florentín , Mónica Miralles

Here, smoothness analysis of almost periodic functions is studied. Analogously to the case of

L^{2} (R)

, the smoothness of the class of Besicovitch almost periodic functions is measured in a classic form by controlling, in some sense, the increments

f (x + h) - f (x)

and in a dual form by the decay of its Fourier–Bohr transform or by its approximation properties. The same problem is also treated considering the time–frequency representation given by the Gabor transform. Some results are given as equivalence of norms between appropriate function spaces.

本文主要研究概周期函数的光滑性分析。与L2(R)的情况类似，Besicovitch类几乎周期函数的平滑性在某种意义上通过控制f(x+h)−f(x)的增量以经典形式测量，并通过其傅里叶-玻尔变换的衰减或其近似性质以对偶形式测量。同样的问题也考虑了由Gabor变换给出的时频表示。给出了适当函数空间间范数等价的一些结果。

引用次数: 0

A 3 × 3 singular solution to the Matrix Bochner Problem with D(W) not of the form ℂ[D] 矩阵Bochner问题的3 × 3奇异解，且D(W)不是形式为[D]

IF 0.6 3区数学 Q2 MATHEMATICS

Journal of Approximation Theory

Pub Date : 2025-11-06 DOI: 10.1016/j.jat.2025.106247

Ignacio Bono Parisi

The Matrix Bochner Problem aims to classify weight matrices whose sequences of orthogonal polynomials are eigenfunctions of a second-order differential operator. A major breakthrough in this direction was achieved in Casper and Yakimov (2022), where it was shown that, under certain natural conditions on the algebra

D (W)

, all solutions arise from Darboux transformations of direct sums of classical scalar weights. In this paper, we study a new 3 × 3 Hermite-type weight matrix and determine its algebra

D (W)

as a

ℂ [D_{1}]

-module generated by

{I, D_{2}}

, where

D_{1}

and

D_{2}

are second-order differential operators. This complete description of the algebra allows us to prove that the weight does not arise from a Darboux transformation of classical scalar weights, showing that it falls outside the classification theorem of Casper and Yakimov (2022). Unlike previous examples in Bono Parisi and Pacharoni (2024) [3, 4], which also do not fit within this classification, the algebra

D (W)

of this weight matrix is not generated by a single differential operator

D

, making it a fundamentally different case. These results complement the classification theorem of the Matrix Bochner Problem by providing a new type of singular example.

矩阵Bochner问题旨在对正交多项式序列为二阶微分算子特征函数的权重矩阵进行分类。Casper和Yakimov（2022）在这一方向上取得了重大突破，他们证明，在代数D(W)的某些自然条件下，所有解都来自经典标量权的直接和的达布变换。本文研究了一个新的3 × 3 hermite型权矩阵，确定了它的代数D(W)为{I，D2}生成的一个[D1]-模，其中D1和D2是二阶微分算子。这种代数的完整描述使我们能够证明权重不是由经典标量权重的达布变换产生的，表明它不属于Casper和Yakimov（2022）的分类定理。与Bono Parisi和Pacharoni(2024)[3,4]中先前的例子不同，这些例子也不适合这种分类，该权重矩阵的代数D(W)不是由单个微分算子D生成的，这是一个根本不同的情况。这些结果通过提供一种新的奇异例子补充了矩阵Bochner问题的分类定理。

{"title":"A 3 × 3 singular solution to the Matrix Bochner Problem with D(W) not of the form ℂ[D]","authors":"Ignacio Bono Parisi","doi":"10.1016/j.jat.2025.106247","DOIUrl":"10.1016/j.jat.2025.106247","url":null,"abstract":"<div><div>The Matrix Bochner Problem aims to classify weight matrices whose sequences of orthogonal polynomials are eigenfunctions of a second-order differential operator. A major breakthrough in this direction was achieved in Casper and Yakimov (2022), where it was shown that, under certain natural conditions on the algebra <math><mrow><mi>D</mi><mrow><mo>(</mo><mi>W</mi><mo>)</mo></mrow></mrow></math>, all solutions arise from Darboux transformations of direct sums of classical scalar weights. In this paper, we study a new 3 × 3 Hermite-type weight matrix and determine its algebra <math><mrow><mi>D</mi><mrow><mo>(</mo><mi>W</mi><mo>)</mo></mrow></mrow></math> as a <math><mrow><mi>ℂ</mi><mrow><mo>[</mo><msub><mrow><mi>D</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>]</mo></mrow></mrow></math>-module generated by <math><mrow><mo>{</mo><mi>I</mi><mo>,</mo><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>}</mo></mrow></math>, where <math><msub><mrow><mi>D</mi></mrow><mrow><mn>1</mn></mrow></msub></math> and <math><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub></math> are second-order differential operators. This complete description of the algebra allows us to prove that the weight does not arise from a Darboux transformation of classical scalar weights, showing that it falls outside the classification theorem of Casper and Yakimov (2022). Unlike previous examples in Bono Parisi and Pacharoni (2024) [3, 4], which also do not fit within this classification, the algebra <math><mrow><mi>D</mi><mrow><mo>(</mo><mi>W</mi><mo>)</mo></mrow></mrow></math> of this weight matrix is not generated by a single differential operator <math><mi>D</mi></math>, making it a fundamentally different case. These results complement the classification theorem of the Matrix Bochner Problem by providing a new type of singular example.</div></div>","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"313 ","pages":"Article 106247"},"PeriodicalIF":0.6,"publicationDate":"2025-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145465905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Journal of Approximation Theory

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀